Question

the graph below shows the altitude of an airplane during a 5 - hour flight.

1. find the rate of change in the first 30 minutes after take off.
2. find the rate of change from one hour and thirty minutes to three hours.
3. find the rate of change from four hours and thirty minutes to when the plane landed.
4. at 6:00 a.m., the temperature is 58°. at 2:00 p.m., the temperature is 76°. find the rate of change in degrees per hour during this time.

Explanation:

Step1: Identify points for Q7

First 30 mins = 0.5 hours. Points: $(0, 0)$ and $(0.5, 24)$ (altitude in thousands of ft).
Rate of change formula: $\frac{\text{Change in altitude}}{\text{Change in time}}$

Step2: Calculate Q7 rate

$\frac{24 - 0}{0.5 - 0} = \frac{24}{0.5} = 48$ (thousand ft per hour)

Step3: Identify points for Q8

1.5 hours to 3 hours. Points: $(1.5, 36)$ and $(3, 36)$.

Step4: Calculate Q8 rate

$\frac{36 - 36}{3 - 1.5} = \frac{0}{1.5} = 0$ (thousand ft per hour)

Step5: Identify points for Q9

4.5 hours to 5 hours. Points: $(4.5, 16)$ and $(5, 0)$.

Step6: Calculate Q9 rate

$\frac{0 - 16}{5 - 4.5} = \frac{-16}{0.5} = -32$ (thousand ft per hour)

Step7: Identify values for Q10

Time difference: 2:00 p.m. - 6:00 a.m. = 8 hours. Temp change: $76^\circ - 58^\circ = 18^\circ$.

Step8: Calculate Q10 rate

$\frac{76 - 58}{8} = \frac{18}{8} = 2.25$ (degrees per hour)

Answer:

1. 48,000 feet per hour
2. 0 feet per hour
3. -32,000 feet per hour
4. $2.25^\circ$ per hour